I have found that sometimes it works well to get permission to do something somewhat smaller or less important than deer hunting (turkey hunting, coyote hunting, shed hunting) first and then be able to grow your relationship with the landowner from there. Not saying those other types of hunting are less important but maybe something you don't care for as much as deer hunting. Majority of the landowners won't even blink if you ask to turkey hunt. Get to know the landowner a little but more importantly let the landowner get to know you better so you can show them you are a likable and trustworthy person.
I got permission from a landowner who owned some ground right next to public by asking if I could walk across his cornfield to get into the back corner of the state ground and he was so confused. He goes, "You don't want to hunt my property?" And I just told him that if I got the opportunity some day to do that, I would be interested but for right now I'm just looking at getting back into the state ground a little easier. We got a long great that first year and I gave him some deer sticks from the doe I shot and he thought that was great. I now have permission on all of his ground.
I also thinks it helps that when you show up to someones door to ask permission that it's probably best not to be dressed in camo from head to toe. I just think that sometimes people can be turned off by that a little bit. I am also a bow hunter so when I ask, I always tell them I will be bow hunting and not gun hunting.
I know Sureshot had a great writeup on this subject last year at some point...I will see if I can find it. He had some awesome points in there. Good luck to you!